An Upper Bound for Ex-Post Sharpe Ratio with Application in Performance Measurement

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The Sharpe ratio and the maximum drawdown (MDD) are two of the most important tools for risk measurement. Existing literature has presented analytical results relating them under geometric Brownian motion. In this paper, we take a data-driven approach to derive a relationship between ex-post Sharpe ratio and MDD. We do not assume any specific distribution of the returns except that they be stationary and ergodic. The relationship we derive can serve as a quick sanity check for black-box performance reports if the Sharpe ratios are estimated by the ex-post Sharpe ratio. Some numerical results are given for illustration.

Raymond H. Chan, Ph.D., The Chinese University of Hong Kong
Kelvin K. Kan, The Chinese University of Hong Kong
Alfred K. Ma, Ph.D., The Chinese University of Hong Kong

The Sharpe ratio and the maximum drawdown (MDD) are two of the most important tools for risk measurement. Existing literature has presented analytical results relating them under geometric Brownian motion. In this paper, we take a data-driven approach to derive a relationship between ex-post Sharpe ratio and MDD. We do not assume any specific distribution of the returns except that they be stationary and ergodic. The relationship we derive can serve as a quick sanity check for black-box performance reports if the Sharpe ratios are estimated by the ex-post Sharpe ratio. Some numerical results are given for illustration.

Raymond H. Chan, Ph.D., The Chinese University of Hong Kong
Kelvin K. Kan, The Chinese University of Hong Kong
Alfred K. Ma, Ph.D., The Chinese University of Hong Kong

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